Let x, y, u, v € Z and d E N. Prove that if x =y (mod d) and u = v(mod d), then xu = yv (mod d).

Q: A legitimate eigenvector of a 10 x 10 matrix could be ГО O 0 0 0 0 0 0 0 0 0 O O 1 2 3 4 5 6 7 8 9…

A: (.)  Eigen vector: Let  be an  matrix. A non - zero  vector  is called an eigen vector corresponding…

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A: We have given a population exponential function for a city:, Where t is in years.To find the value…

Q: 4. Let p> 2 be prime. Show that there exists an integer n such that n² + 1 is a multiple of p if and…

A: We use the fact that if gcd(a,p)=1 then a^{p-1}= 1 (mod p)

Q: -5 1. Determine an equation in factored form for the polynomial function represented by the graph. 5…

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Q: For the vector field (x, y, z) evaluate the line integral along the curve made of three adjacent…

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Q: (5) Let ƒ : (a, ∞) → R be such that lim xf(x) = L, L € R. Prove that lim f(x) = 0. X48 x→∞

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Q: The above is the graph of a system of linear inequality constraints. The graph is unbounded and its…

A: Given:

Q: Solution"). 7. Consider the following system whose motion has no damping and whose solution y(t) is…

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Q: Let U1 and U2 be two linearly independent solutions of the second-order linear differential equation…

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Q: 22.3 Let E= Q(√2,√√3, √5). Find [E: Q] and a basis for E over Q.

A: Let .Find  and find a basis for  over .

Q: Evaluate the line integral fo H dr, where H = (y, -z, x) and C is a circle of radius 3, lying in the…

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Q: Graph the system of inequalities. Tell whether the system is bounded or unbounded and list each…

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Q: 6. A relation R on a set X is called a total order if it is antisymmetric, reflexive, transi- tive,…

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Q: Let G = GL(2, R) and let g = (a) Letz 8 J Write down all the elements of the right coset Kr. 3 (b)…

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Q: 8. A spring with spring constant 8 Newtons/meter is hung from the ceiling. A mass of 2 kg. is…

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Q: Solve the reccurence relation a_n = sqrt (a(n-2) / a(n-1)) with initial conditions a_0 = 8, a_1 = 1…

A: We have to solve the recurrence relation a_n = sqrt (a(n-2) / a(n-1)) with initial conditions a_0 =…

Q: Define a digit to be an element of the set (0, 1, 2, 3, 4, 5, 6, 7, 8, 9) Show that any real number…

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Q: Show that if c>l, then มะ ) Converges

A: We shall use the Cauchy Condensation test for solving this problem.

Q: r = 10 1 5

A: We find the 5th root of the 10 by using Newton Raphson method.The equationwe use the formula

Q: What is the volume of the solid obtained by rotating the region bounded by y = x², x = 0 and y = 4…

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Q: 4. Given differential equation y" + y = csc (t) a. Find the complimentary solution y, that solves…

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Q: Please show if each function f  is an inverse. If yes, give the inverse function with the process to…

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Q: Draw the edges needed in order to make the following graph complete. De E F Clear All Draw: Line…

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Q: -30 -20 За Use the empirical rule to find the probability corresponding to the shaded region above.…

A: Using the empirical rule we have to find the probability of the shaded region.

Q: Please draw the level curves of the following shown below. Show your work: a) z = x² b) z = x² + y²…

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Q: Find the missing side length. Assume that all intersecting sides meet at right angles. Be sure to…

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Q: 1. Use the definition to write the improper integral A. lim B B. lim t> 1¹ C. lim t>1 1 1 x+1 1 x+1…

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Q: A store has wrapping paper on sale. One package is 3 rolls of 2- Itx 8 ft for $6.00. 2 Another…

A: To determine which package is a better buy, let's calculate the cost per square foot for each…

Q: -15x-15y-z=12 -9x-25y-2z=51 12x+15y+z=-18 Select the correct choice below​ and, if​ necessary,…

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Q: You are purchasing a car and have the option to pay $25,000 in cash (upfront) OR assume a lease with…

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Q: Show that F(s) est ds if F(s) for ->O as $18 t>o

A: According to the question,

Q: Find all points (x,y) where f(x,y) has a possible relative maximum or minimum. Then, use the…

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Q: Number of Students in College Algebra Classes 289 3127 4101 Key: 28 means 28 students In the College…

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Q: Approximate the mass of the homogeneous lamina that has the shape of given surface S and density…

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Q: Let A = {1,2,3,4} and B = {5, 6, 7}. Let f be the relation f = {(1,5). (2,5), (3,6), (?, ?)} where…

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Q: 1. Solve the congruence 2. Solve the congruence x² + 1 = 0 mod 13³. x³ - 2x² - 7x+3=0_mod 7². 3.…

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Q: 6. Consider the mass spring system whose motion y(t) is governed by y" + 4y' + 3y = 30 cos 3t, y(0)…

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Q: 20. f(x) = π, g(x) = cos² x + sin² x 21. f(x) = x³, g(x) = x²|x|

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Q: Use the graph of Ax)- y 2 -2 0 -2 fixi = a) -4 <x<3 IN d) -4<x<3 2 1 Ob) no solution Oc) x=-4 X+4 x…

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Q: How about 8-10? Will surely give a thumbs up afterwards.

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Q: A sequence (n)-1 is said to oscillate if lim inf n<lim supen and both lim inf n and lim sup In are…

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Q: Why'd you choose 1/5?

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Q: Formulate a dynamic programming recursion that minimize the costs related to the opening new…

A: As per the question, G-Motor, a leading manufacturer of airplane engines, faces the strategic…

Q: I understand the inverse to find 1/2x+3.... but why invert 35/3

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Q: Hsu-Mei wants to save $3,000 for a down payment on a car. To the nearest dollar, how much will she…

A: Let  be the present value you need to invest in an account.

Q: 2. Let S be the surface given by r(u, v) = (u, u² + v², v). Find the equation of the tangent plane…

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Q: Naturalists find that the populations of some kinds of predatory animals vary periodically. Assume…

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Q: Motorcycle Noise A recent study of 42 motorcycles found that the average noise pollution in decibels…

A: Sample size Mean Standard deviation Confidence

Q: Map at least 5 key points and then sketch a graph of f(x) = −3 cos ; (2x + 1). Show your work…

A: We have to draw the graph of given function

Q: Part A: 527 Hundred's place: Part B: 54673 Ten thousands place: Place: Part C: 93 Ten's Place: Ten's…

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